On the Improperness Index of a Polynomial Matrix and Some of Its Properties

Abstract

The column properness of a polynomial matrix is one of the most important properties for the interactor of the linear multivariable systems. However it is observed that the properties of the column improperness play a more important role rather than those of the column properness in the derivation of the interactor. In this paper, the improperness index and d_i-improperness index which indicate the measure of the column improperness are defined and some of their properties are discussed. For this purpose, the “Γ-matrix” is defined using the coefficient matrices of the polynomial matrix, which palys the basic role for the derivation of the interactor. The relation between the improperness index and the rank of Γ-matrix of the same polynomial matrix is highlighted.